The telescope focal length is the distance from the primary objective (the main lens or mirror in the system) and the point where focus occurs.

We assume telescopes used for astronomy will be focused at infinity. This means we can assume the image plane will be at the focal point. Eyepieces are used to view a piece of this image plane. Different eyepeices will show a different sized piece of the image plane at different magnifications.

The telescope aperture is the diameter of the primary objective. A larger aperture will capture more light as well as produce a sharper, higher resolution, image than a smaller aperture.

The entire telescope aperture is used to create each piece of the image at the image plane.

The telescope's focal ratio is the ratio between the focal length and the aperture. It is often refered to as an f/number. A smaller f/number is said to be "faster" than a larger f/number. This is slang from the photography world where a smaller f/number allows you to shoot with a faster shutter speed.

The eyepiece focal length is the distance between the principal plane of the eyepiece and the point where focus occurs. This value is almost always printed on the side of the eyepiece or otherwise known. Shorter focal length eyepieces give more magnified views than longer focal length eyepieces.

If you desire a specific exit pupil or magnification, you can use the following equations to estimate the eyepiece focal length required.

The eyepiece apparent field of view (AFOV) is the angular size of the image produced by the eyepiece. This value represents how large the image will appear to your eye regardless of the telescope specifications. Eyepieces with larger apparent field of views will be able to show more sky than narrow eyepeice designs.

The field stop is the effective diameter of the visible field at the focal plane of the eyepiece. The field stop defines the size of the telescope's image plane that can be seen by the eyepiece. This diameter can be imposed by a physical stop, or by internal eyepiece components. The maximum size of the field stop is very often constrained by the inside diameter of the eyepiece barrel.

The actual, or true, field of view is the angular size of the piece of sky that can be seen through an eyepiece. There are two equations that can be used to calculate the field of view. The more accurate equation uses the eyepiece field stop. This assumes the field stop of the eyepiece is at the focal plane of the telescope, and that the telescope is focused at infinity.

In cases where the eyepiece field stop is not known, you can use the apparent field of view of the eyepiece to estimate the true field of view.

The exit pupil is a measure of the diameter of the column of light that emerges from the eyepiece. This is the light that enters your eye. You can easily see the exit pupil if you look at your eyepiece from a few feet away while your telescope is pointed at a daytime sky.

When the exit pupil is larger than your eye's pupil, not all of the light from the telescope image enters your eye. This can be desirable, especially for a refractor, if you want an increased field of view at the expense of lost light. For telescopes with a central obstruction, however, exit pupils larger than your eye's pupil can show the obstruction. You can easily see this if you use a long focal length eyepiece in an obstructed telescope durring the day when your eye's pupil is not fully dialated. You will see a dark spot in the middle of the field of view. The same eyepiece will behave different at night when your eye's pupil is larger. A 7mm maximum is usually assumed for exit pupil because this is the average size of a young person's fully dialated pupil. Your own eyes are likely different than the 7mm rule of thumb.

If you have astigmatism in your eyes, it will be less apparant when viewing with smaller exit pupils. For example, you might notice astigmatism at 7mm, but not at 5mm or smaller.

The value given for magnification represents how much bigger the image appears in the eyepiece compared to when viewed with the naked eye.

There is a maximum limit to magnification related to the maximum resolution possible with a given telescope. This is often given as 50x per inch of aperture. This ends up being equivalent to an exit pupil of 0.5mm. Magnifying beyond this limit will just be magnifying a fuzzy image. Some people will actually start to notice the shaddows caused by the floaters in their eyes when using very tiny exit pupils.

Even if the telescope is able to resolve very high magnifications, the atmosphere usually prevents good views when magnifying higher than about 300x.